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We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…

Quantum Physics · Physics 2009-10-31 A. Carlini , A. Hosoya

The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the…

In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…

Quantum Physics · Physics 2020-11-11 Stephen Bruce Sontz

Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling…

Quantum Physics · Physics 2026-02-20 Marcin Płodzień

I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…

Quantum Physics · Physics 2009-11-10 W. H. Zurek

The possibility to recover the which-way information, for example in the two slit experiment, is based on a natural but implicit assumption about the position of a particle {\it before} a position measurement is performed on it. This…

Quantum Physics · Physics 2007-06-13 Bruno Galvan

The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…

Quantum Physics · Physics 2017-10-17 Daniela Frauchiger , Renato Renner

In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g.…

Quantum Physics · Physics 2024-06-19 G. B. Lesovik

According to the subjective Bayesian interpretation of quantum theory (QBism), quantum mechanics is a tool that an agent would be wise to use when making bets about natural phenomena. In particular, the Born rule is understood to be a…

In this work we establish a novel approach to the foundations of relativistic quantum theory, which is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal…

Mathematical Physics · Physics 2025-11-17 Maik Reddiger , Bill Poirier

In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence…

Numerical Analysis · Mathematics 2024-10-08 Nicholas Defilippis , Shari Moskow , John C. Schotland

Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…

Quantum Physics · Physics 2026-01-13 James Fullwood , Zhihao Ma , Zhen Wu

The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…

High Energy Physics - Theory · Physics 2009-07-22 Don N. Page

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers…

Quantum Physics · Physics 2018-10-26 Charles T. Sebens , Sean M. Carroll

We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ($\sim10^{-25}\,\mathrm{s}$) currently accessible at high-energy colliders. We focus on targeted…

High Energy Physics - Phenomenology · Physics 2026-01-05 Antony Valentini , Mira Varma

In a previous article [1] we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach there is no "emergence", but the structure of…

Quantum Physics · Physics 2022-02-09 Alexia Auffeves , Philippe Grangier

The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory…

Quantum Physics · Physics 2025-12-08 Mikołaj Sienicki , Krzysztof Sienicki

We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…

Quantum Physics · Physics 2026-03-31 Lauro Mascarenhas , Vinicius N. A. Lula-Rocha , Marco A. S. Trindade

Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…

Information Theory · Computer Science 2016-06-23 Allan F. Randall

Quantum cognition in decision-making is a recent and rapidely growing field. In this paper we develop an expected utility theory in a context of non-classical (quantum) uncertainty. We replace the classical state space with a Hilbert space…

Physics and Society · Physics 2017-08-29 Vladimir V. Danilov , Ariane Lambert-Mogiliansky , Vassily Vergopoulos